Invertible analytic functions on Drinfeld symmetric spaces and universal extensions of Steinberg representations
| Autor: | Lennart Gehrmann |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Mathematics - Algebraic Geometry
Computational Mathematics Mathematics (miscellaneous) Mathematics - Number Theory Applied Mathematics Mathematik FOS: Mathematics Number Theory (math.NT) Representation Theory (math.RT) Computer Science::Digital Libraries Algebraic Geometry (math.AG) Mathematics - Representation Theory Theoretical Computer Science |
| Popis: | Recently, Gekeler proved that the group of invertible analytic functions modulo constant functions on Drinfeld's upper half space is isomorphic to the dual of an integral generalized Steinberg representation. In this note we show that the group of invertible functions is the dual of a universal extension of that Steinberg representation. As an application, we show that lifting obstructions of rigid analytic theta cocycles of Hilbert modular forms in the sense of Darmon--Vonk can be computed in terms of $\mathcal{L}$-invariants of the associated Galois representation. The same argument applies to theta cocycles for definite unitary groups. Comment: 19 pages, new section about the Dedekind-Rademacher cocycle, to appear in Research in the Mathematical Sciences |
| Databáze: | OpenAIRE |
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